Volume Calculator - 12 Shapes, 8 Units, Live Weight
Use this effective volume solver to calculate the volume of any shape - box, cylinder, sphere, cone, pyramid, capsule and more - with instant output in m³, litres, gallons, cubic feet and more. Add a material to get total weight, and see real-world equivalents for tanks, rooms, containers and pools.
Advanced options
Total Volume
Volume in All Units
| Unit | Value | Notes |
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Capacity and Real-World Comparison
| Comparison | Value |
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How to Use Volume Calculator for Boxes, Cylinders, Spheres and Every Other Shape
Pick a shape, enter the dimensions, choose a unit and (optionally) pick a material. The calculator returns volume in 8 units, weight, capacity in litres and gallons, and instant reference comparisons.
Volume Formulas for Every Shape
These are the exact formulas the calculator uses. Reference them whenever you need to verify a result by hand.
| Shape | Formula | Example |
|---|---|---|
| Box / Cuboid | V = L × W × H | 2 × 1.5 × 1 = 3 m³ |
| Cube | V = a³ | 2³ = 8 m³ |
| Cylinder | V = π × r² × h | π × 0.5² × 2 = 1.571 m³ |
| Sphere | V = (4/3) × π × r³ | (4/3) × π × 0.5³ = 0.524 m³ |
| Cone | V = (1/3) × π × r² × h | (1/3) × π × 0.5² × 1.5 = 0.393 m³ |
| Pyramid (rect) | V = (1/3) × L × W × h | (1/3) × 2 × 2 × 3 = 4 m³ |
| Capsule | V = π × r² × (4r/3 + L) | π × 0.5² × (0.667 + 2) = 2.094 m³ |
| Hemisphere | V = (2/3) × π × r³ | (2/3) × π × 0.5³ = 0.262 m³ |
| Tube (hollow cyl) | V = π × (RO² - RI²) × h | π × (0.25 - 0.16) × 3 = 0.848 m³ |
| Triangular prism | V = (1/2) × b × h × L | (1/2) × 1 × 0.8 × 3 = 1.2 m³ |
| Trapezoidal prism | V = ((A + B)/2) × h × L | ((2 + 3)/2) × 1 × 5 = 12.5 m³ |
| Cone frustum | V = (πh/3) × (r1² + r1r2 + r2²) | π × 2/3 × (0.09 + 0.18 + 0.36) = 1.319 m³ |
| Ellipsoid | V = (4/3) × π × a × b × c | (4/3) × π × 0.5 × 0.4 × 0.6 = 0.503 m³ |
Volume Unit Conversions
Quick reference for converting between the eight volume units this calculator supports.
| From 1 unit | m³ | Litres | cm³ | US gal | UK gal | ft³ | in³ | yd³ |
|---|---|---|---|---|---|---|---|---|
| 1 m³ | 1 | 1,000 | 1,000,000 | 264.172 | 219.969 | 35.315 | 61,024 | 1.308 |
| 1 litre | 0.001 | 1 | 1,000 | 0.264 | 0.220 | 0.0353 | 61.024 | 0.00131 |
| 1 cm³ | 0.000001 | 0.001 | 1 | 0.000264 | 0.000220 | 0.0000353 | 0.061 | 0.0000013 |
| 1 US gallon | 0.003785 | 3.785 | 3,785 | 1 | 0.833 | 0.134 | 231 | 0.00495 |
| 1 UK gallon | 0.004546 | 4.546 | 4,546 | 1.201 | 1 | 0.161 | 277.42 | 0.00595 |
| 1 ft³ | 0.028317 | 28.317 | 28,317 | 7.481 | 6.229 | 1 | 1,728 | 0.0370 |
| 1 in³ | 0.0000164 | 0.0164 | 16.387 | 0.00433 | 0.00360 | 0.000579 | 1 | 0.0000214 |
| 1 yd³ | 0.764555 | 764.555 | 764,555 | 201.974 | 168.179 | 27 | 46,656 | 1 |
Material Density Reference
Densities used by the weight calculator. Multiply your volume by the density to get mass.
| Material | Density (kg/m³) | Density (lb/ft³) | Typical use |
|---|---|---|---|
| Water (fresh) | 1,000 | 62.4 | Tanks, pools, containers |
| Seawater | 1,025 | 64.0 | Marine, coastal |
| Concrete | 2,400 | 150 | Slabs, footings, columns |
| Cement (loose) | 1,440 | 90 | Bags, silos |
| Dry sand | 1,600 | 100 | Aggregate, fill |
| Gravel | 1,500 | 94 | Driveways, drainage |
| Soil (packed) | 1,400 | 87 | Backfill, excavation |
| Topsoil | 1,300 | 81 | Gardening, landscaping |
| Asphalt | 2,300 | 144 | Roads, driveways |
| Steel | 7,850 | 490 | Structural, containers |
| Aluminium | 2,700 | 169 | Lightweight structures |
| Glass | 2,500 | 156 | Windows, tanks |
| Brick (dense) | 1,900 | 119 | Wall construction |
| Wood - pine | 500 | 31 | Framing, crates |
| Wood - oak | 700 | 44 | Furniture, flooring |
| Milk | 1,030 | 64.3 | Dairy tanks |
| Cooking oil | 920 | 57.4 | Commercial kitchens |
| Petrol | 750 | 46.8 | Fuel storage |
| Diesel | 850 | 53.1 | Fuel storage |
How the Volume Calculator Works
Every result uses standard geometric formulas verified by quantity surveyors. Here is the exact process behind the calculator.
- Shape formula is applied - each of the 12 shapes has its own specific formula listed in the reference table above.
- Dimensions are converted to metres internally so all formulas work in SI units.
- Volume in m³ is the base - from this, all other units are derived using standard conversion factors.
- Litres = m³ × 1,000. US gallons = m³ × 264.172. UK gallons = m³ × 219.969.
- Weight = volume × density when a material is selected. All densities are given in kg/m³.
- Real-world comparisons are computed by dividing your volume by standard reference volumes (bathtub, wheelbarrow, drum, etc).
Frequently Asked Questions About Volume Calculation
How do I calculate the volume of a box?
Multiply length × width × height. All three must be in the same unit. For example, a box 2 m long, 1.5 m wide and 1 m high has a volume of 3 m³ (3 cubic metres), which is 3,000 litres or 792.5 US gallons. The calculator handles all unit conversions automatically.
How do I calculate volume in litres?
First get the volume in cubic metres (m³), then multiply by 1,000. So 1 m³ = 1,000 litres. If you have dimensions in centimetres, first convert to metres (divide by 100), then apply the shape formula. A 100 × 100 × 100 cm box is 1 m³ = 1,000 litres.
What is the volume of a cylinder?
Volume = π × radius² × height. For a cylinder with a 0.5 m radius and 2 m height, that is 3.14159 × 0.25 × 2 = 1.571 m³. If you have the diameter instead, halve it to get the radius first. The calculator lets you enter either radius or diameter.
How many litres in a cubic metre?
There are exactly 1,000 litres in 1 cubic metre. This is because 1 litre is defined as 1 cubic decimetre (10 × 10 × 10 cm = 1,000 cm³), and 1 m³ contains 1,000 such decimetres. So a 2 m³ tank holds 2,000 litres.
How many gallons in a cubic metre?
A cubic metre contains 264.17 US gallons or 219.97 UK (imperial) gallons. The UK gallon is larger than the US gallon, which is why there are fewer of them. Always specify which gallon system you mean - the calculator shows both to avoid confusion.
How do I calculate the volume of an irregular shape?
You cannot apply a simple formula to a truly irregular shape. The best approach is to break it into regular sub-shapes, calculate each one separately, then add the volumes together. Alternatively, use the "average dimensions" method - measure the longest and shortest sides in each direction and use the average. The ellipsoid shape handles most rounded irregular forms reasonably well.
What is the difference between volume and capacity?
Volume is the space occupied by an object. Capacity is the amount a container can hold. For a solid box, they are the same. For a hollow container, the capacity is the internal volume, which is smaller than the external volume (the difference is the wall thickness). The Tube shape handles the wall thickness for containers.
How do I work out the weight of a volume of material?
Multiply volume by density. Every material has a standard density - water is 1,000 kg/m³, concrete is 2,400 kg/m³, sand is 1,600 kg/m³. So 1 m³ of concrete weighs 2,400 kg (2.4 tonnes), and 1 m³ of water weighs 1,000 kg (1 tonne). The calculator does this automatically when you select a material.
What is a cubic metre in practical terms?
A cubic metre is a cube 1 m × 1 m × 1 m. In practical terms, it is about: 1,000 litres of water (about 4 large bathtubs), or 1.3 cubic yards (the unit used for concrete delivery), or 35.3 cubic feet. It weighs 1 tonne if filled with water, and 2.4 tonnes if filled with concrete.
How do I measure volume in a tank or container?
Measure the internal dimensions - not the external. For a rectangular tank, use Length × Width × Height. For a cylinder tank, use π × radius² × height. For a horizontal cylinder (like a capsule), use the Capsule shape. For a tank with a domed top or bottom, use the Hemisphere shape for each end and add them separately.
Why does concrete volume shrink after mixing?
Dry concrete ingredients (cement, sand, gravel) occupy more volume than the wet concrete they produce. When water is added, the particles pack more tightly and fill air voids. That is why dry material volume is roughly 1.54 times the wet volume. The Volume Calculator gives you the wet volume; for materials planning, multiply by 1.54 as a dry-volume factor.
Can I use this calculator for cooking or baking?
Yes for geometric shapes like pans and moulds. For a round cake tin with a 20 cm diameter and 5 cm depth, use the Cylinder shape. For a rectangular tin, use the Box shape. Enter the internal dimensions in cm - the calculator returns millilitres (cm³) and litres.
How do I convert between volume and weight for soil or gravel?
Multiply volume by density. Dry topsoil is about 1,300 kg/m³, packed soil is 1,400 kg/m³, dry gravel is 1,500 kg/m³. So 1 m³ of gravel weighs roughly 1.5 tonnes. When ordering gravel or soil by weight, always add 10% for moisture and compaction variation.
How many wheelbarrows in a cubic metre?
A standard builder's wheelbarrow holds about 65 - 100 litres, with 80 litres being typical. That means 1 m³ = 12 - 15 wheelbarrow loads of concrete, sand or soil. The calculator shows this comparison automatically in the results table.
References & Standards
- ISO 80000-3 - Quantities and units: Space and time (volume definitions)
- NIST Handbook 44 - Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices
- BS 350 - Conversion factors and tables
- ASTM E380 - Standard Practice for Use of the International System of Units (SI)
- CRC Handbook of Chemistry and Physics - Densities of Common Materials
- ISO 3506 - Mechanical properties of corrosion-resistant stainless steel fasteners
- AS 1379 - Specification and supply of concrete (Australia)
- NIS 550 - Nigerian Industrial Standard Building Code